Page 117 - Mathematics Coursebook

11.3 Comparing quantities

11.3 Comparing quantities

It is o&en useful to use percentages to compare proportions. Schools’ results are the same!
Here is an example. Two schools both have 40 students gaining the
top grade in an exam. Schools’ results are different!
You might think that both schools are similar, but the $rst school
entered 50 students and the second school entered 200. Which headline is correct?

In the $rst school 80% achieved the top grade. In the second school only
20% did so.

Worked example 11.3

A student scored 21 out of 30 in a maths test and 54 out of 75 in a science test. Which was her
better score?

7
Maths score = 21 = 10 Write the maths score as a fraction and simplify it.
30
7 70
10 = 100 = 70% Change the fraction to a percentage.
Science score = 54 = 18 = 72 = 72% Do the same with the science score
75 25 100
The scores were similar. The science score is slightly better, but there is only a
difference of 2%.

) Exercise 11.3

1 a Change these test marks to percentages.
i 4 out of 10 ii 17 out of 25 iii 24 out of 80 iv 20 out of 60
b Which was the best mark?
2 In class A, 17 out of 25 students were absent at least one day this year.
In class B the figure was 14 out of 20. In class C it was 18 out of 24.
a Work out the percentage who were absent in each class
b Which class had the worst record for absences?
3 A 400 g pack of couscous contains 116 g of carbohydrate.
A 250 g bag of maize flour contains 195 g of carbohydrate.
A 1 kg bag of wheat flour contains 640 g of carbohydrate.
Use percentages to work out the amount of carbohydrate in each.

4 Mujib has $40 and Prakash has $120. Each of them spends $24.
Work out the percentage of their money that each of them has spent.
5 In a baby clinic, the nurse weighed 20 baby boys and 30 baby girls.
Their weights were recorded as ‘underweight’, ‘normal’ or ‘overweight’.
The results are in this table.
Underweight Normal Overweight
Boys 5 6 9
Girls 6 12 12

116 11 Percentages